{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,2,20]],"date-time":"2023-02-20T03:49:48Z","timestamp":1676864988564},"reference-count":23,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2008,8]]},"abstract":"<jats:p> In this paper, we concern representations of symplectic rook monoids R. First, an algebraic description of R as a submonoid of a rook monoid is obtained. Second, we determine irreducible representations of R in terms of the irreducible representations of certain symmetric groups and those of the symplectic Weyl group W. We then give the character formula of R using the character of W and that of the symmetric groups. A practical algorithm is provided to make the formula user-friendly. 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